Sully is having a party and wants to fill his swimming pool. If he only uses his hose, it takes 3 hours more than if he only uses his neighbor's hose. If he uses both hoses together, the pool fills in 5 hours. How long does it take for each hose to fill the pool (in hr)?

It takes the neighor's hose 3 hours to fill the pool and it takes Sully's hose 6 hours to fill the pool if each filled alone.

Step-by-step explanation:

This is a work problem, and the way these are done is to figure the amount that each can do based on how much can get done in a single hour.  

First thing, in order to have only one variable, we have to put one hose in terms of the other hose.  

We know that it takes the neighbor's hose a certain amount of time (there's our unknown) to fill the pool and that it takes Sully's hose that same time plus 3 hours.

neighbor's hose can get the job done in x time

Sully's hose can get the job done in x + 3 time

Now we will figure out how much each can do in a single hour.

If the neighbor's hose takes x hours to fill the pool, then it can get

of the pool filled in 1 hour.

If Sully's hose takes x + 3 hours to fill the pool, then it can get

of the pool filled in 1 hour.

The sum of these takes 2 hours total and 1/2 of the pool gets filled in 1 hour.

Our equation then is:

This equation states in words:

"the amount of the pool that the neighbor's hose can fill in an hour plus the amount of the pool that Sully's hose can fill in an hour will fill half the pool".

Solving for x will give us that time.

Begin to solve this by finding the LCM of those denominators and getting rid of the fractions by reducing.  The LCM will be 2x(x + 3).  Multiplying each term by that LCD looks like this:

In the first term the x's cancel out, in the second term the (x + 3) cancels out, and in the last term the 2's cancel out leaving us with:

and simplifying gives us:

This is a quadratic that will have to be factored to solve for those values of x.  Combine like terms and get everything on one side to get:

Factor this however you find easiest to get the values:

x = 3 hours and x = -2 hours

We all know that the 2 things in math that will never EVER be negative are times and distances/measures, so we can disregard the -2 and say that

x = 3 hours.  

To answer our question, then;

It takes the neighbor's hose 3 hours to fill the pool; it takes Sully's hose 3+3 hours = 6 hours to fill the pool.

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